Details

Time bar (total: 12.3s)

analyze1.1s (9%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
12.5%87.4%0.1%5
18.7%81.1%0.1%6
18.7%76.5%4.8%7
28.1%66.3%5.6%8
35.1%55%9.9%9
36.3%50.9%12.8%10
42.1%42.4%15.5%11
47.5%33.8%18.7%12
48.8%30.7%20.6%13
51.8%25.6%22.5%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample48.0ms (0.4%)

Algorithm
intervals
Results
11.0ms36×body2048valid
10.0ms168×body128valid
6.0ms15×body4096valid
3.0ms15×body1024valid
3.0ms18×body512valid
2.0ms28×body128nan
1.0msbody256valid
0.0msbody128invalid
Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify137.0ms (1.1%)

Algorithm
egg-herbie
Rules
808×fma-neg_binary64
379×associate-/l*_binary64
361×div-sub_binary64
341×fma-def_binary64
224×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01120
12318
23918
36918
410718
517818
627918
738218
854718
958718
1085518
11124718
12111718
13103518
14104318
15105118
16107718
17109318
18112918
19113118
20114318
21105018

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
32.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
32.5b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
Compiler

Compiled 58 to 30 computations (48.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
0.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
0.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
22.3b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

series217.0ms (1.8%)

Counts
4 → 96
Calls

4 calls:

82.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
80.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
44.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
10.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

rewrite33.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt_binary64
41×*-un-lft-identity_binary64
31×add-cube-cbrt_binary64
20×sqrt-prod_binary64
19×prod-diff_binary64
Counts
4 → 120
Calls

4 calls:

9.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
7.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
4.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
3.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

simplify378.0ms (3.1%)

Algorithm
egg-herbie
Rules
682×fma-neg_binary64
364×cancel-sign-sub-inv_binary64
248×distribute-rgt-neg-in_binary64
220×distribute-lft-neg-in_binary64
172×distribute-rgt-in_binary64
Counts
216 → 237
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02725568
16834769
224844515
345214514
449154514
549904514
650004514
749994514
849324514

prune171.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2298237
Fresh000
Picked011
Done000
Total2299238
Error
3.9b
Counts
238 → 9
Alt Table
StatusErrorProgram
32.5b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
32.7b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) (/.f64 a (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))
44.1b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 c a (*.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
43.8b
(/.f64 (*.f64 -2 b_2) a)
43.9b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
30.3b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
40.6b
(*.f64 -1/2 (/.f64 c b_2))
44.3b
(/.f64 (*.f64 -1/2 (/.f64 (*.f64 c a) b_2)) a)
30.4b
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
Compiler

Compiled 5866 to 1649 computations (71.9% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
0.1b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
12.1b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series648.0ms (5.3%)

Counts
3 → 24
Calls

3 calls:

396.0ms
(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
230.0ms
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
21.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite34.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
138×times-frac_binary64
105×add-sqr-sqrt_binary64
104×*-un-lft-identity_binary64
72×add-cube-cbrt_binary64
26×associate-/r*_binary64
Counts
3 → 167
Calls

3 calls:

7.0ms
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
4.0ms
(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
1.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify165.0ms (1.3%)

Algorithm
egg-herbie
Rules
886×associate-/l*_binary64
389×fma-def_binary64
386×associate-/r/_binary64
180×associate-/l/_binary64
164×cancel-sign-sub-inv_binary64
Counts
191 → 240
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02506076
15815621
219395407
353355407

prune139.0ms (1.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2355240
Fresh437
Picked011
Done011
Total23910249
Error
0.0b
Counts
249 → 10
Alt Table
StatusErrorProgram
44.9b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
43.8b
(/.f64 (*.f64 -2 b_2) a)
30.5b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) (/.f64 a (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
30.4b
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
32.5b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
30.3b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
40.6b
(*.f64 -1/2 (/.f64 c b_2))
48.1b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
30.5b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
40.4b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (/.f64 (neg.f64 c) b_2))))
Compiler

Compiled 6778 to 1878 computations (72.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
0.1b
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
0.2b
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
12.1b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series1.0s (8.4%)

Counts
3 → 20
Calls

3 calls:

484.0ms
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
305.0ms
(sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
250.0ms
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))

rewrite42.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt_binary64
56×*-un-lft-identity_binary64
52×times-frac_binary64
50×sqrt-prod_binary64
38×add-cube-cbrt_binary64
Counts
3 → 132
Calls

3 calls:

15.0ms
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
6.0ms
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
4.0ms
(sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))

simplify201.0ms (1.6%)

Algorithm
egg-herbie
Rules
757×times-frac_binary64
705×associate-/l*_binary64
350×fma-def_binary64
348×fma-neg_binary64
245×associate-/l/_binary64
Counts
152 → 191
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02395562
15765017
217094838
349914838
451804838

prune135.0ms (1.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New2570257
Fresh077
Picked011
Done022
Total25710267
Error
0.0b
Counts
267 → 10
Alt Table
StatusErrorProgram
44.9b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
43.8b
(/.f64 (*.f64 -2 b_2) a)
30.5b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) (/.f64 a (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
30.4b
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
32.5b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
30.3b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
40.6b
(*.f64 -1/2 (/.f64 c b_2))
48.1b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
30.5b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
40.4b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (/.f64 (neg.f64 c) b_2))))
Compiler

Compiled 9318 to 1588 computations (83% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 a (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
0.2b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) (/.f64 a (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
0.3b
(*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
12.1b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series3.7s (30%)

Counts
3 → 36
Calls

3 calls:

2.1s
(/.f64 a (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
1.3s
(*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
225.0ms
(/.f64 (*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) (/.f64 a (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))

rewrite73.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
102×times-frac_binary64
94×add-sqr-sqrt_binary64
92×*-un-lft-identity_binary64
78×cbrt-prod_binary64
58×add-cube-cbrt_binary64
Counts
3 → 199
Calls

3 calls:

14.0ms
(/.f64 (*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) (/.f64 a (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
9.0ms
(*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
5.0ms
(/.f64 a (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

simplify371.0ms (3%)

Algorithm
egg-herbie
Rules
619×fma-def_binary64
334×associate-/l*_binary64
218×associate-*r*_binary64
210×*-commutative_binary64
197×fma-neg_binary64
Counts
235 → 342
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
043513085
1109911251
239559922
349369922
449549922

prune270.0ms (2.2%)

Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New3990399
Fresh066
Picked011
Done033
Total39910409
Error
0.0b
Counts
409 → 10
Alt Table
StatusErrorProgram
44.9b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
43.8b
(/.f64 (*.f64 -2 b_2) a)
30.5b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) (/.f64 a (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
30.4b
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
32.5b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
30.3b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
40.6b
(*.f64 -1/2 (/.f64 c b_2))
48.1b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
30.5b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
40.4b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (/.f64 (neg.f64 c) b_2))))
Compiler

Compiled 19481 to 3347 computations (82.8% saved)

regimes1.5s (12.5%)

Accuracy

Total 10.3b remaining (98.8%)

Threshold costs 0b (0%)

Counts
121 → 3
Compiler

Compiled 12956 to 6562 computations (49.4% saved)

bsearch87.0ms (0.7%)

Steps
ItersRangePoint
9
3.6580647694951247e-10
0.0001945844493844541
1.0024243244806623e-8
6
-1.5954525291034723e+84
-3.655528475908628e+83
-1.514362293518873e+84
Compiler

Compiled 4 to 3 computations (25% saved)

simplify32.0ms (0.3%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02344
13344
24644
35444
45944
56044
66044

end1.0ms (0%)

Compiler

Compiled 33 to 21 computations (36.4% saved)

sample1.7s (13.9%)

Algorithm
intervals
Results
349.0ms1126×body2048valid
342.0ms5244×body128valid
167.0ms684×body1024valid
159.0ms413×body4096valid
64.0ms355×body512valid
49.0ms806×body128nan
22.0ms178×body256valid
15.0ms250×body128invalid
Compiler

Compiled 236 to 140 computations (40.7% saved)

Profiling

Loading profile data...